Factorizable Current Algebras at All Momenta

Abstract

Factorizable representations (of isospin \textonehalf{}) of the $S{U}_{2}$ algebra of conserved currents on the physical Hilbert space of states having all momenta are studied. Without any constraints on the Schwinger term except those arising from current conservation, it is demonstrated that the currents can be expressed as functions of a set of basic variables, and that their commutation relations, as well as the covariance conditions, can be written in terms of these basic variables themselves and a symmetric Schwinger operator. The Schwinger operator is itself fairly well determined by the covariance conditions and is such as to make the algebra of fields inconsistent with factorizability. Finally, it is shown that a no-go theorem holds even for representations at finite momenta, making the mass spectrum unphysical.